11 papers
Operator level soft edge to bulk transition in -ensembles via canonical systems
Vincent Painchaud, Elliot Paquette
The stochastic Airy and sine operators, which are respectively a random Sturm-Liouville operator and a random Dirac operator, characterize the soft edge and bulk scaling limits of…
Anisotropic local law for non-separable sample covariance matrices
Zhou Fan, Renyuan Ma, Elliot Paquette +1
We establish local laws for sample covariance matrices $K = N^{-1}\sum_{i=1}^N \g_i\g_i^*$ where the random vectors $\g_1, \ldots, \g_N \in \R^n$ are independent with common covari…
Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression
Hugo Latourelle-Vigeant, Elliot Paquette
This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in rand…
High-Dimensional Privacy-Utility Dynamics of Noisy Stochastic Gradient Descent on Least Squares
Shurong Lin, Eric D. Kolaczyk, Adam Smith +1
The interplay between optimization and privacy has become a central theme in privacy-preserving machine learning. Noisy stochastic gradient descent (SGD) has emerged as a cornersto…
Eigenvalue distribution of the Neural Tangent Kernel in the quadratic scaling
Lucas Benigni, Elliot Paquette
We compute the asymptotic eigenvalue distribution of the neural tangent kernel of a two-layer neural network under a specific scaling of dimension. Namely, if $X\in\mathbb{R}^{n\ti…
Bulk asymptotics of the Gaussian -ensemble characteristic polynomial
Gaultier Lambert, Elliot Paquette
The Gaussian -ensemble (GE) is a fundamental model in random matrix theory. In this paper, we provide a comprehensive asymptotic description of the characteristic polynomia…